How do I mirror an object using the mirror modifier?
You have to position your 3D Cursor away from the cylinder, then press Shift+Ctrl+Alt+C and choose the 3rd option- Origin to 3D Cursor. Next add a Mirror Modifier and choose the axis. Remember that the mirrored object appears on the same opposite distance from the origin, that's why you have to put your origin away from the Cylinder center, otherwise you will not be able to see any change, as your mirrored object will appear in the same position as your mesh.